A Study of the Radio Spectrum of Mrk 421

We present the results of a spectral analysis using simultaneous multifrequency (22, 43, 86, and 129 GHz) very long baseline interferometry (VLBI) observations of the Korean VLBI Network on BL Lac object, Markarian 421. The data we used were obtained from 2013 January to 2018 June. The light curves showed several flux enhancements with global decreases. To separate the variable and quiescent components in the multifrequency light curves for milliarcsecond-scale emission regions, we assumed that the quiescent radiation comes from the emission regions radiating constant optically thin synchrotron emissions (i.e., a minimum flux density with an optically thin spectral index). The quiescent spectrum determined from the multifrequency light curves was subtracted from the total CLEAN flux density, yielding a variable component in the flux that produces the time-dependent spectrum. We found that the observed spectra were flat at 22-43 GHz, and relatively steep at 43-86 GHz, whereas the quiescent-corrected spectra are sometimes quite different from the observed spectra (e.g., sometimes inverted at 22-43 GHz). The quiescent-corrected spectral indices were much more variable than the observed spectral indices. This spectral investigation implies that the quiescent-spectrum correction can significantly affect the multifrequency spectral index of variable compact radio sources such as blazars. Therefore, the synchrotron self-absorption B-field strength (B SSA) can be significantly affected because B SSA is proportional to the fifth power of turnover frequency.